derivative (-x^2-7)/((x^2-7)^2)

Lösung

ableitung von

\frac{- x ^{2} - 7}{( x ^{2} - 7 ) ^{2}}

- \frac{2 x ( - x ^{2} - 21 )}{( x ^{2} - 7 ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{- x ^{2} - 7}{( x ^{2} - 7 ) ^{2}})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( - x ^{2} - 7 ) ( x ^{2} - 7 ) ^{2} - \frac{d}{d x} ( ( x ^{2} - 7 ) ^{2} ) ( - x ^{2} - 7 )}{( ( x ^{2} - 7 ) ^{2} ) ^{2}}

\frac{d}{d x} (- x^{2} - 7) = - 2 x

\frac{d}{d x} ((x^{2} - 7)^{2}) = 4 x (x^{2} - 7)

= \frac{( - 2 x ) ( x ^{2} - 7 ) ^{2} - 4 x ( x ^{2} - 7 ) ( - x ^{2} - 7 )}{( ( x ^{2} - 7 ) ^{2} ) ^{2}}

Vereinfache

\frac{( - 2 x ) ( x ^{2} - 7 ) ^{2} - 4 x ( x ^{2} - 7 ) ( - x ^{2} - 7 )}{( ( x ^{2} - 7 ) ^{2} ) ^{2}} : - \frac{2 x ( - x ^{2} - 21 )}{( x ^{2} - 7 ) ^{3}}

= - \frac{2 x ( - x ^{2} - 21 )}{( x ^{2} - 7 ) ^{3}}

\int \frac{3 x ^{2}}{( 2 x ^{3} - 4 ) ^{2}} d x

in v erse l a pl a ce \frac{2 s - 1}{s ^{2} - 6 s + 18}

\frac{d}{d t} (12 t)

\int_{0}^{1} e^{- s t} d t

\int (x^{x}) d x